Not Understanding Time Dilation - mk 2.

[PAllen]

OK, message heard! I'll see if I can reframe it away from any gravity.

Before you do that, would you please respond to my comments regarding your previous scenario in post #42. My comments are in posts #45, #49 and #55.

Also see my post #48. I threw in humorous wording, but the content is serious.

 

[Dale]

OK, message heard! I'll see if I can reframe it away from any gravity.

Thanks, I think that you can learn a lot that will help your understanding. I think that there are 3 scenarios that are worth considering here:
1) Two perpetually inertial observers
2) Standard twin's paradox
3) One clock at rest and one in uniform circular motion

The last one may be particularly interesting for you since it is pretty easy to use a rotating coordinate system where the circular-motion clock is at rest, and doing so allows you to gently introduce some of the very useful GR-related math without the complications of gravity and curvature. But I would approach them in order and not jump to 3) until you are comfortable with 1) and 2).

 

[cmb]

Before you do that, would you please respond to my comments regarding your previous scenario in post #42. My comments are in posts #45, #49 and #55.

#45 - I've no problem with that, but it isn't quite what I meant.

#49 - Sorry, I did indeed miss that one in the melee: "If so, then you have overlooked the fact that the orbiting clock is not inertial, it is always accelerating toward the earth.." This is an interesting point, and is why I initially shyed away from using accelerating ships in free space. However, if I drill down into this point, can you explain why 'inertial' differs from 'accelerating'? There is no 'acceleration' component in the equation given on wiki, just a gravity and a velocity term.

#55 - Almost, that is about it, but a slightly different flavour. If there is to be a noticeable time dilation effect once some time-piece/person/whatever returns to 'earth', then by how much is it? It doesn't appear to be objective, because if we watch a clock 'elsewhere' in some other frame, adjusted so it appears to keep time, then the time dilation when that clock returns to Earth should be a function of the path it takes to get back to earth, not how longit has been there building up a 'desynch'.

PAllen #48 - It seemed similar to an earlier reply. "the funny clock would now be going fast compared to the ground clock, with a time difference accumulating only from when the satellite's motion changed from what the funny clock was adjusted for" .. but what about the notion that as the guy on the satellite has been watching it, it has been gaining time over the clock on the ground? I thought we'd agreed that'd happen earlier, which'd make it 'time-in-orbit' dependent?

 

[PAllen]

PAllen #48 - It seemed similar to an earlier reply. "the funny clock would now be going fast compared to the ground clock, with a time difference accumulating only from when the satellite's motion changed from what the funny clock was adjusted for" .. but what about the notion that as the guy on the satellite has been watching it, it has been gaining time over the clock on the ground? I thought we'd agreed that'd happen earlier, which'd make it 'time-in-orbit' dependent?

That was all meant to be clarified with the introduction of an unadjusted clock. The adjusted clock is gaining time over the colocated unadjusted clock. It will not be seen as gaining time over the ground clock, by the satellite observer.

 

[ghwellsjr]

#45 - I've no problem with that, but it isn't quite what I meant.

If it's not quite what you meant, then what did you mean? Where did I go wrong?

#49 - Sorry, I did indeed miss that one in the melee: "If so, then you have overlooked the fact that the orbiting clock is not inertial, it is always accelerating toward the earth.." This is an interesting point, and is why I initially shyed away from using accelerating ships in free space. However, if I drill down into this point, can you explain why 'inertial' differs from 'accelerating'? There is no 'acceleration' component in the equation given on wiki, just a gravity and a velocity term.

In the context of Special Relativity (assuming no gravity), "inertial" and "accelerating" are opposites. Inertial means you are experiencing no acceleration which means you could be traveling in a straight line at a constant velocity. Non-inertial means that you are either changing your speed or changing your direction or both.

#55 - Almost, that is about it, but a slightly different flavour. If there is to be a noticeable time dilation effect once some time-piece/person/whatever returns to 'earth', then by how much is it? It doesn't appear to be objective, because if we watch a clock 'elsewhere' in some other frame, adjusted so it appears to keep time, then the time dilation when that clock returns to Earth should be a function of the path it takes to get back to earth, not how longit has been there building up a 'desynch'.

Time dilation is absolutely objective although it may be complicated to calculate but if you can be precise in exactly what happens to a clock, its time dilation with respect to any given Frame of Reference can be exactly calculated.

If in your scenario in post #42, an orbiting clock has to be adjusted so that it keeps time with an Earth bound clock, then when you return it to earth, there will be no sudden jump in time related to how long it was orbiting. If we can assume that the trip is done instantly, then there will be no change in the time and both clocks will match up. But from that point on, since the orbiting clock had been adjusted, it will start accumulating an increasing time difference.

I was just speculating in post #45 that it might be possible to put a clock in orbit around a planet such that no adjustment was necessary and that the two clocks would always remain in synch.

But I want to ask you again: are you thinking of the orbiting clock like the traveling twin in the Twin Paradox?